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A028576

a(n) = (1/(4*n)) * Sum_{d|n} mu(n/d) * binomial(2*d, d)^2.

1, 4, 33, 304, 3175, 35556, 420665, 5176000, 65664000, 853367900, 11309870605, 152342891952, 2080240006923, 28738242567524, 401024083514775, 5645275548076800, 80084088088568947, 1143862232096407392, 16437995698573558421, 237520818846111947600, 3449065945198414208745

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OFFSET

1,2

COMMENTS

Conjecture: a(n) is divisible by n and 3*a(n) by n^2. - F. Chapoton, Feb 25 2026

LINKS

Michel Marcus, Table of n, a(n) for n = 1..800

MATHEMATICA

A028576[n_] := DivisorSum[n, MoebiusMu[n/#]*Binomial[2*#, #]^2 &]/(4*n);

Array[A028576, 25] (* Paolo Xausa, Mar 02 2026 *)

PROG

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*binomial(2*d, d)^2)/(4*n) \\ Michel Marcus, Jun 15 2013